Related papers: Lagrangian isotopies in Stein manifolds

We extend constructions and results of Damian to get topological obstructions to the existence of closed monotone Lagrangian embeddings into the cotangent bundle of a space which is the total space of a fibration over the circle.

Geodesics in the space of positive Lagrangian submanifolds are solutions of a fully non-linear degenerate elliptic PDE. We show that a geodesic segment in the space of positive Lagrangians corresponds to a one parameter family of special…

We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumption, this can happen only on topological spheres.

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a…

We show that simply connected contact manifolds that are subcritically Stein fillable have a unique symplectically aspherical filling up to diffeomorphism. Various extensions to manifolds with non-trivial fundamental group are discussed.…

For a geometrically finite hyperbolic surface of infinite volume we write down the spectral decomposition for the Laplacian on 1-forms, generalize the Kudla and Millson's construction of hyperbolic Eisenstein series and other related…

We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…

This paper explores the existence and properties of \emph{basic} eigenvalues and eigenfunctions associated with the Riemannian Laplacian on closed, connected Riemannian manifolds featuring an effective isometric action by a compact Lie…

We prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat moduli space of its boundary marked surface is a Lagrangian…

We derive constraints on Lagrangian concordances from Legendrian submanifolds of the standard contact sphere admitting exact Lagrangian fillings. More precisely, we show that such a concordance induces an isomorphism on the level of…

Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…

We define a Chern- Simons Lagrangian for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. We propose exact N-body eigenstates, set up a…

A Lagrangian system with two degrees of freedom is considered. The configuration space of the system is a cylinder. A large class of periodic solutions has been found. The solutions are not homotopy equivalent to each other.

Techniques of gauge theory are used to define and compute an invariant of certain diffeomorphisms of 4-manifolds. The invariant vanishes for any diffeomorphism which is smoothly isotopic to the identity. As an application, we give the first…

Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial…

We define a nonnegative integer $\la(L,L_0;\phi)$ for a pair of diffeomorphic closed Lagrangian surfaces $L_0,L$ embedded in a symplectic 4-manifold $(M,\w)$ and a diffeomorphism $\phi\in\Diff^+(M)$ satisfying $\phi(L_0)=L$. We prove that…

We study curvature properties of four-dimensional Lorentzian manifold with two-symmetry property. We then consider Einstein-like metrics, Ricci solitons and homogeneity over these spaces.

We define obstructions which obstruct topological pseudo-isotopies from being isotopic to isotopies in dimension four. These match the smooth obstructions of Hatcher-Wagoner for smooth pseudo-isotopies, and accordingly are valued in certain…

We study "circular net" (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are…

Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…